This is relatively easy, but it requires an astute observation. You use this quite a bit later in topology so I guess it's a good challenge question.
NOTE: If you have already seen the solution to this, please don't ruin the fun! This is aimed at people who haven't seen a lot of topology before.
Problem: Define to be the set of all square-summable real sequences equipped with the metric . Prove that this metric space is separable.
Note: Separable means it contains a countable dense subset. Also, while my book calls this it is most commonly known as .